Laminated conductor



April 15, 1958 s. P. MORGAN, JR 2,831,172 LAMINATED CONDUCTOR FiledSept. 11, 1952 2 She ets-Sheet 1 FIG.

FIG. 2

x (s, 3 F/LL FACTOR INVENTOR S. P MORGAN JR By J. 64%,?

ATTORNEY 7'2 ATTENUAT/ON l/V ARE/TRAP) UNITS RELAT/VE THICKNESS OF/NNERSTACK April 15, 1958' s. P. MORGAN, JR 2,831,172

LAMINATED CONDUCTOR Filed Sept. 11, 1952 2 Sheets-Sheet 2 RELATIVE CORERAD/US x (5, sJ/b F/LL acre/e 62 l I I I I INVENTOR 5. P MORGAN JR.

ATTORNEY application that when a conductor Veins W Pate? 2,831,172LAMINATED CONDUCTOR Samuel P. Morgan, Jr., Morristown, N. .L, assiguorto Bell Telephone Laboratories, Incorporated, New York, N; Y., acorporation of New York Appiication September 11, 1952, Serial No.309,023 2 Claims. C1. 333*96 This invention relates to electricalconductors and more particularly to composite conductors formed of amultiplicity of insulated conducting portions and which have come to beknown as Clogston conductors.

It is an object of this invention to improve the current distribution incomposite conductors of the type comprising one or more stacks eachincluding a large number of insulated conducting portions, andparticularly to effect such improvement by the proportioning of thestacks.

In a copending application of A. M. Clogston, Serial No. 214,393, filedMarch 7, 1951, now Pat. No. 2,769,148, October 30, 1956, there aredisclosed a number of composite conductors, each of which comprises amultiplicity of insulated conducting elements of such number,dimensions, and disposition relative to each other and to theorientation of the electromagnetic wave being propagated therein as toachieve a more favorable distribution of current and field within theconducting material. In one specific embodiment disclosed in Figs. 7Aand 7B of the Clogston application, two coaxially arranged compositeconductors (stacks) are separated by dielectric material, each of thecomposite conductors comprising a multiplicity of thin metal laminationsinsulatedfrom one another by layers of insulating material, the smallestdimensions of the laminations being in the direction perpendicular totboth the direction of wave propagation and the magnetic vector. Eachmetal lamination is many times (for example 10, 100, or even 1000 times)smaller than the factor 6 which is called one skin thickness or one skindepth. The distance '6 is given by the expression where '6 is expressedin meters, is the frequency in cycles per second, ,a is the permeabilityof the metal in henries per meter, and ois the conductivity in mhos permeter. The factor 6 measures the distance in which the current and fieldpenetrating into a slab of the material many times 6 in thickness willdecrease by one neper'; e. their amplitude will become equal toMei-0.3679 times their amplitude at the surface of the slab.

It is pointed out in the above-mentioned Clogston has such a laminatedstructure, a wave propagated along the conductor at a velocity in theneighborhood of a certain critical value will penetrate further into theconductor (or completely through it) than it would penetrate into asolid conductor of the same material, resulting in a more uniformcurrent distribution in the laminated conductor and consequently lowerlosses. In the case where the cable is not magnetically loaded, thecritical velocity for the type of structure just described is determinedby the thicknesses of the metal and insulating laminae and thedielectric constant of the insulation between the laminae 2 in thecomposite conductors. The critical velocity can be maintained by makingthe dielectric constant of the main dielectric, that is the dielectricmaterial between the we eoinposite conductors, lowing relationship:

Where a, is the dielectric-constant of the main dielectric elementbetween the two conductors in farads per meter, e is the dielectricconstant of the insulating material between the laminae 6f theconductors in farads per meter, is the thickness of one of the metallaminae in meters and t is thethi'ck-ne'ss of the insulating lamina inmeters. The insulating laminae are also made very thin and an optimumthieknes's for certain structures of this general type is that in whicheach insulating lamina is onehalf the thickness of a metal lamina. Thiscondition does not exist, however, in all cases.

It has been discovered that in unloaded Clogston con- Various laminae inthe composite conductors. Above this certain frequency the attenuationconstant rises. In the description which follows, the attenuation con-'stant in this uniform or fiat portion of the curve of attenuatio'nconstant vs. frequency will be known as the low frequency attenuationconstant although, as mentioned above, in practice this region mayextend up to many megacycl'es.

The present invention is based on the discovery that this low frequencyattenuation constant can be minimized for various optimum conditions.Assuming a fixed outer radius and that the electrical constants of themain dielectric and of the inner and outer stacks are tired, for each'value of fill factor x, that is, the ratio of the total stack thicknessto the outer radius of the composite conductor, there is a definiteradius of core a and distribution of the laminated material betweeninner and outer stacks 'for minimum low frequency at-, tenuation.

The invention will be more readily understood by referring to thefollowing description taken in connection with the accompanying drawingsforming a part thereof, in which:

Fig. 1 is an end view of a coaxial composite conductor in accordanceWith the invention, the outer conductor or stack comprising amultiplicity of metal laminations separated by insulating material andthe inner conductor or stack being similar in this respect to the outerconductor, the two stacks being separated by an intermediate or maindielectric member;

Fig. 2 is a longitudinal view, with portions broken away, of thecomposite conductor of Fig. 1;

Fig. 3 is a graph of attenuation constant vs. frequency for a compositeconductor of the type shown in Figs. 1 and 2;

Fig. 4 is a graph of r (a constant proportional to atthat is, the withlamoistacks satisfy the foland 2 show, .by way of example, a conductor10 inaccordance with the invention, Fig. 1 being an end view and Fig. 2being a longitudinal view. The conductor 1t) comprises a central core 11(which may be either of metal or dielectric material), an innercomposite conductor or stack 12 formed of many laminations of metal 13spaced by insulating material 14, an outer composite conductor or stack15 formed of a multiplicity of layers of metal 16 spaced by insulatingmaterial 17 and separated from the inner conductor 12 by an intermediateor main dielectric member 18, and an outer sheath 19 of metal or othersuitable shielding material. As disclosed in the above-mentionedClogston application, each of the metal layers 13 and 16 is made verythin compared to the skin depth of the conductor being used, which, forexample, can be copper, silver, or aluminum. The insulating layers 14and 17 are also made very thin and may be of any suitable material.Examples of satisfactory materials are: polyethylene, polystyrene,quartz and polyfoam. Preferably, the insulating layers are of the orderof onehalf ,the thickness of each metal layer, although this is notnecessarily true in all cases. The inner conductor or stack 12 has 10 or100 or more metal layers 13 and the outer conductor or stack 15 has anumber of metallic layers 16 of the same order of magnitude as thenumber of metal layers 13 but, as will be pointed out below, there arenot necessarily the same number of conductors in the two stacks. Sincethere are a large number of insulating and metallic layers, it makes nodifierence whether the first or the last layer in each stack (12 or 15)is of metal or of insulation.

As pointed out above, certain optimum relationships exist in unloadedClogston conductors or cables of the general type just described. Theseoptimum relationships make it possible to select various ratios andproportions of elements within the stack which will give the minimum lowfrequency attenuation constant. These relationships are optimum only inthe low frequency portion of the graph of attenuation constant vs.frequency 1. As shown in Fig. 3, which presents a typical curve ofattenuation constant a vs. frequency 1, there is a low frequency portion20 (which extends in practice from a frequency of a few kilocycles tomany megacycles) which is substantially flat and parallel to thehorizontal axis and a high frequency portion 21 which curves upward. Itshould be understood that for each particular configuration of cablethere is a different curve of low frequency attenuation constant vs.frequency, the curve designated A in Fig. 3 being only one of a familyof curves each one of which has the same general shape but which vary inthe height of the low frequency portion 20 above the horizontal axis andthe extent of this horizontal portion. This invention is based on thediscovery that in unloaded Clogston cables, such as, for example, of thegeneral type shown in Figs. 1 and 2, there are optimum conditions whichgive a minimum height for the portion 20 of the curve A above thehorizontal axis, or, in other words, which give a minimum low frequencyattenuation constant.

Before pointing out these optimum conditions a general relationship willbe set forth. In this relationship the notation is as follows: a=radiusof inner core 11. b=inner radius of outer shield 19. =inner radius ofmain dielectricls. zouter radius of main dielectric 18. S =p z1=lhlClnSSof inner stack 12. s =b- =thickness of outer stack 15. t =thickness ofeach conducting lamina 13 or 16 (called W by Clogston in theabove-mentioned Clogston application Serial No. 214,393).

L-thickness of each insulating lamina 14 or 17 (called t by Clogston inhis application Serial No. 214,393). 0=t /(t +t :fraction of stacks 12and filled with conducting material 13 or 16.

e =dielectric constant of main dielectric member 18. E =dielectricconstant of insulating laminae 14 and 17.

e=e /(10) =average of dielectric constant of stacks 12 and 1S.

tzthe permeability of free space (41rX10" henries per meter).

cr =COIldUCtlViiY of the conducting laminae 13 and 16.

2: Bar; average conductivity of stacks 12 and 15.

For all configurations of the cables shown in Figs. 1 and 2 it isassumed that the relationship which has come to be known as Clogstonscondition that is, the relationship of Equation 2, above, is exactlysatisfied. The conducting laminae are considered as beinginfiuitestimally thin compared to the skin depth; the thinner thelaminae, the greater the frequency range over which this assumption isvalid. Furthermore, the impedances of both the inner core 11 and theouter shield 19 are made so high that the currents, if any, flowing inthe core and shield are negligible compared to the currents in thestacks. No restrictions, however, are placed on the values of a, p p andb.

The low frequency attenuation constant of the principle mode in cablesof the type shown in Figs. 1 and 2 is given y cz= fi l 2'61) where r isthe lowest positive root of the equation: 1 t( 0( P2/ 1( o( P2/ P2 1('P2/ l( t( P2/ r( i( )No( m/ t( o( m/ g m 1( p1/ 1( 1( m/ 1( p1 InEquation 4, I and N are Bessel and Neumann functions of orders 0 and 1as indicated. Given the dimensions of the cable a [1 p and p the lowestvalue of r which satisfies Equation 4 can be obtained by graphical ornumerical means. By varying the ratios 11/ b, p /b, and p /b and solvingfor r in a number of different cases, it is possible to determine howdepends on the geometric proportions of the cable. If, for example, agiven fill factor ees is specified, then the proportions of the cablecan be completely determined by giving the relative radius a/b of theinner core and the fraction s /(s +s of the total laminated materialwhich is in the inner stack. By varying a/b and s 4-5 and calculatingthe corresponding values of r, one can find the values of a/b and s /(s+s which make r as small as possible, consistent with the given fillfactor.

Pig. 4 shows a curve obtained by assigning specific values to the fillfactor x and which represents the lowest attenuation that can beobtained for a given fill factor. in this curve the attenuationinarbitrary units (r is plotted against x. The curve of Fig. 4 may berepresented approximately by the following equation:

As shown in this figure, the higher values of fill factor produce lower,values of attenuation and the lowest value exists for a fill factor ofunity, or, in other words, when the conductor 10 is completely filledwith laminations.

Fig. 5 shows the optimum value of the relative core radius for variousfill factors. In this figure, the relative core radius that is, theratio of the inner diameter of the inner stack 12 (5 to the outer radius12 of the outer stack 15-(s is plotted against the fill factor x. As inFig. 4 this relation exists throughout the region represented by theportion 20 of the curve in Fig. 3. The curve in Fig. 5 obeyssubstantially the equation:

Fig. 6 shows the optimum relative thickness of the inner stack, s /(s +splotted against the fill factor x in the low frequency attenuationregion 20 of the curve of Fig. 3. The curve shown in Fig. 6 obeysapproximately the equation The optimum relationships shown in Figs. 5and 6 make it possible to design a cable for minimum low frequencyattenuation. Fig. 4 shows that in the absence of magnetic loading, ifthe fill factor is at ones disposal, the minimum attenuation is to beobtained with a fill factor of unity, that is, with the cable completelyfilled with laminations. However, there are some disadvantages of havingthe fill factor unity and given some other fill factor it is possible toobtain from the curves shown in Figs. 5 and 6 the relative core radiusand the relative thickness of the inner stack to produce minimum lowfrequency attentuation.

What is claimed is:

1. A composite elongated electromagnetic wave conductor adapted for usewith high frequency electromagnetic waves comprising an inner stack ofinsulated elongated conducting members and an outer stack of insulatedelongated conducting members surrounding the inner stack and separatedtherefrom by non-magnetic dielectric material having a thickness greaterthan that of the insulation between said conducting members, therelationship of relative core radius and fill factor x being givensubstantially by the equation:

6 in which a is the inner radius of the inner stack, bis the outerradius of the outer stack and the fill factor x is equal to where s isthe thickness of the inner stack and s is the thickness of the outerstack, each of the insulated conducting members in said inner and outerstacks being thinner than the skin depth of penetration of waves intothe material of said conducting members at the highest frequency ofoperation of said conductor.

2. A composite elongated electromagnetic wave conductor adapted for usewith high frequency electromagnetic waves comprising an inner stack ofinsulated elongated conducting members and an outer stack of insulatedelongated conducting members surrounding the inner stack and separatedtherefrom by non-magnetic dielectric material having a thickness greaterthan that of the insulation between said conducting members, therelative thickness s /(s +s of the inner stack and the fill factor xhaving substantially the relationship material of said conductingmembers at the highest frequency of operation of said conductor.

References Cited in the file of this patent UNITED STATES PATENTSSilbermann Feb. 5, 1929 Clogston Oct. 30, 1956

